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Open problems in mathematical physics

Alan A Coley
2017 Physica Scripta  
We present a list of open questions in mathematical physics.  ...  After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly  ...  Summary of problems in mathematical physics The hardest part, perhaps, is making the number of open questions in mathematical physics add up to 42.  ... 
doi:10.1088/1402-4896/aa83c1 fatcat:zviukujzvfg5vmb62ynbkeutci

Open Problems in Mathematics with John Nash

Michael Rassias
2017 EMS Newsletter  
to prepare together the book Open Problems in Mathematics.  ...  problems in mathematics.  ... 
doi:10.4171/news/106/13 fatcat:epkjdmywt5f5zpxowo62hpjk24

Mathematical open problems in Projected Entangled Pair States [article]

J. Ignacio Cirac, José Garre-Rubio, David Pérez-García
2019 arXiv   pre-print
The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.  ...  Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems.  ...  However in 2D the analogue problems are quite open. First of all, there is no known solution of the local approximation problem.  ... 
arXiv:1903.09439v1 fatcat:e6ejobfwqvc2vgdyhzjckmydym

Five open problems in compressible mathematical fluid dynamics

Denis Serre
2013 Methods and Applications of Analysis  
The problems below are motivated by some of the works I did in the past. They deal with the dynamics of compressible fluids, either viscous or inviscid.  ...  They are not worth a million dollars, even not a penny, but they are interesting in their own.  ...  The open problems are countless, and our choice of five of them is strongly biased by our own mathematical interest and previous research.  ... 
doi:10.4310/maa.2013.v20.n2.a6 fatcat:5kmmrbtqzzaafkqb4chdcuud7y

Selection principles in mathematics: A milestone of open problems [article]

Boaz Tsaban
2007 arXiv   pre-print
We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics.  ...  evolving field of mathematics.  ...  This is one of the major open problems in the field.  ... 
arXiv:math/0312182v4 fatcat:o3llea6ey5f5xamcivxs3rwtwm

About Open Problems [chapter]

Çetin Kaya Koç
2014 Open Problems in Mathematics and Computational Science  
about unsolved, open problems in mathematical and computation sciences, directly from the scientists who are rigorously investigating them.  ...  The motivation of the Open Problems in Mathematical and Computational Sciences Conference was to enable and encourage the academic community, particularly young researchers and Ph.D. candidates, to hear  ...  One purpose of the Open Problems in Mathematical and Computational Sciences Conference is to encourage, motivate, and excite the mathematical and computational sciences community to discuss open problems  ... 
doi:10.1007/978-3-319-10683-0_1 fatcat:bsjz3cnk5vdhphs7zm7xb76m24

Communication Ability in Resolving Open-Ended Problem in Mathematics

Anis Ni'matus Sholihah, Riyadi Riyadi, Triyanto Triyanto
2020 International Journal of Multicultural and Multireligious Understanding  
The purpose of research was to know student's communication abilities in solving open-ended problems with the material equation and quadratic function.  ...  Based on research analysis show that: (1) written communication of the students in solving problems have different solutions; (2) the student with high communication ability is better at open-ended problem  ...  One of problem in mathematics is mathematics open problems.  ... 
doi:10.18415/ijmmu.v7i7.1771 doaj:0d317862840a469a917ef70f8769a373 fatcat:fj44ubwtszeknjmhwm2gjgzw2a

The Discrete Logarithm Problem [chapter]

René Schoof
2016 Open Problems in Mathematics  
In this expository paper we discuss several generalizations of the discrete logarithm problem and we describe various algorithms to compute discrete logarithms.  ...  For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z/pZ) * is at present a very difficult problem.  ...  Exponential algorithms Following ideas in [11, section 7] , we consider the following general problem. It is a natural extension of the discrete logarithm problem. Problem.  ... 
doi:10.1007/978-3-319-32162-2_12 fatcat:7hrvoz54tbfbji5rnalx2rssui

Open Tasks in Mathematics: Experiences with one Problem Field

Erkki Pehkonen
2018 Magistra Iadertina  
With its aid, our purpose is to show how open teaching acts in practice.  ...  In this paper, the task "Number Triangle" stands for problem fields. The problem field in question is planned by the author to be used in the Finnish comprehensive school.  ...  The problem offered me a good structure on the implementation of open problems in school instruction.  ... 
doi:10.15291/magistra.1487 fatcat:ywlwyu2x7nhntluzx4pei7cdiu

Using open problems and cooperative methods in mathematics education

András Ambrus, Krisztina Barczi-Veres
2015 LUMAT  
Two aspects are taken into consideration in connection with mathematical problem solving: open problems and cooperative teaching.  ...  Roughly speaking we can differentiate between two main styles in teaching mathematics: either the focus is on the students or the focus is on mathematics as a science.  ...  In our experiment opening problems goes in this direction 2.  ... 
doi:10.31129/lumat.v3i1.1048 fatcat:i46xkaxinbbt7brgq5lufzo6em

The role of open-ended problems in mathematics education

H. Wu
1994 Journal of Mathematical Behavior  
Open-ended problems have become a popular educational tool in mathematics education in recent years.  ...  Since mathematical research is nothing but a daily confrontation with open-ended problems, the introduction of this type of problems to the classroom brings mathematical education one step closer to real  ...  The isoperimetric inequality is one of the most profound inequalities in mathematics, both in terms of its intrinsic significance and the impact it has exerted on the development of mathematics, past and  ... 
doi:10.1016/0732-3123(94)90044-2 fatcat:qjbd632yozeulomoiufx2kfzsa

Hadwiger's Conjecture [chapter]

Paul Seymour
2016 Open Problems in Mathematics  
This is a tremendous strengthening of the four-colour theorem, and is probably the most famous open problem in graph theory. * Supported by ONR grant N00014-10-1-0680 and NSF grant DMS-1265563.  ...  Introduction The four-colour conjecture (or theorem as it became in 1976), that every planar graph is 4-colourable, was the central open problem in graph theory for a hundred years; and its proof is still  ...  This remains open.  ... 
doi:10.1007/978-3-319-32162-2_13 fatcat:v3wuu2dy55cyldjdpens53tuku

Some open problems in mathematical two-dimensional conformal field theory [article]

Yi-Zhi Huang
2017 arXiv   pre-print
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.  ...  In this note, we discuss some open problems in this program. Some of the problems are well known. The others are what the author is interested in and believes to be important.  ...  for the successful solutions of mathematical conjectures and problems.  ... 
arXiv:1606.04493v2 fatcat:g63t64hzifd4jkpyhz7smhgqt4

Open Problems in Logical Dynamics [chapter]

Johan van Benthem
2006 Mathematical Problems from Applied Logic I  
This paper is a survey of conceptual issues and open mathematical problems emanating from this development.  ...  'Open problems' in new areas like this may be of several different sorts.  ...  We mention some open problems in those areas that seem relevant to our concerns in the preceding sections.  ... 
doi:10.1007/0-387-31072-x_3 fatcat:f5il7g4k6zcdndjrl3ymqaetl4

The evolution of mathematical explorations in open-ended problem-solving situations

Victor V. Cifarelli, Jinfa Cai
2005 Journal of Mathematical Behavior  
Focus on Learning Problems in Mathematics, 27(3), illustrated and explained several characteristics of the solvers' mathematical explorations in open-ended problem situations.  ...  Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems?  ...  Acknowledgements The research discussed in this paper was supported, in part, by grants from the Spencer Foundation and the University of North Carolina.  ... 
doi:10.1016/j.jmathb.2005.09.007 fatcat:q7nynxggtfay5eivtxafjbue4a
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